The use of electrical measurements in prior art downhole applications, such as logging while drilling (LWD) and wireline logging applications, is well known. Such techniques may be utilized, for example, to determine a subterranean formation resistivity, which, along with formation porosity measurements, may be used to indicate the presence of hydrocarbons in the formation. It is known in the art that porous formations having a high electrical resistivity often contain hydrocarbons, such as crude oil, while porous formations having a low electrical resistivity are often water saturated. It will be appreciated that the terms resistivity and conductivity are often used interchangeably in the art. Those of ordinary skill in the art will readily recognize that these quantities are reciprocals and that one may be converted to the other via simple mathematical calculations. Mention of one or the other herein is for convenience of description, and is not intended in a limiting sense.
Microresistivity measurements of a subterranean formation are commonly made by focusing an electrical current into the formation. Microresistivity sensors generally include at least three electrodes: a guard electrode, a return electrode, and a measuring electrode which may be deployed in and electrically isolated from the guard electrode. In use, an AC voltage is commonly applied between the guard electrode and the return electrode, which results in an alternating current being passed through the formation between the guard and return electrodes. Meanwhile, the measuring electrode is commonly held at the same potential as the guard electrode. The alternating current in the measuring electrode is monitored and tends to be indicative of the resistivity of the formation opposing the electrode. As is known to those of ordinary skill in the art, the formation resistivity Ra may be expressed mathematically, for example, as follows:
                              R          a                =                  k          ⁢                                    Δ              ⁢                                                          ⁢              V                        I                                              Equation        ⁢                                  ⁢        1            
where k is a geometric factor, ΔV represents the potential difference between the measuring electrode and a reference point, and I represents the current in the measuring electrode. The formation resistivity Ra is sometimes referred in the art as an apparent resistivity indicating that the computed quantity is at least partially related to the true formation resistivity.
In downhole drilling applications it is often desirable to make microresistivity measurements at multiple depths (at least two depths) of investigation into the formation. The benefits of making measurements at multiple depths of investigation are numerous. For example, measurements at multiple depths may enable environmental effects, such as the presence of an invasion zone, to be identified. Measurements at multiple depths of investigation may also improve the accuracy (or reduce the uncertainties) in formation dip calculations. Furthermore, measurements at multiple depths provide data redundancy and may therefore improve accuracy and data quality control.
Various tool configurations are disclosed in the prior art for making microresistivity measurements at multiple depths of investigation. For example, U.S. Pat. No. 4,594,552 to Grimaldi et al discloses a wireline tool in which three longitudinally spaced measuring electrodes are deployed in the guard electrode. The depth of investigation at each measuring electrode is said to be a function of the longitudinal distance between that electrode and the return electrode.
U.S. Pat. Nos. 5,235,285 and 5,339,037 to Bonner et al. disclose a logging while drilling tool including a wound toroidal core antenna deployed about the tool body and a plurality longitudinally spaced current measuring electrodes deployed in the tool body. Similar to the Grimaldi tool, the depth of investigation at each measuring electrode is said to be a function of the longitudinal distance between that electrode and transmitter.
U.S. Pat. No. 7,046,010 to Hu et al teaches a pad mounted electrode configuration that makes use of five concentric electrodes and a central current sensing electrode. The concentric electrodes can be used either for current focusing or current return with the outer boundary of the outermost electrode defining a current focusing area. Increasing the current focusing area is said to increase the depth of investigation.
One common feature of the above-referenced tools is that they require a large number of electrodes in order to make microresistivity measurements at multiple depths of investigation. In general, in the prior art the number of achievable depths of investigation tends to be approximately proportional to the number of electrodes utilized. One drawback with the use of additional electrodes (to achieve additional depths of investigation) is that they tend to increase the complexity of the sensor, which in turn tends to increase costs and decrease the reliability of microresistivity tools employing such sensors. Therefore, there is a need for a microresistivity sensor that enables measurements to be made at multiple depths of investigation without requiring the use of a large number of electrodes.